Comparative statics | EPFL Graph Search

In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter. As a type of static analysis it compares two different equilibrium states, after the process of adjustment (if any). It does not study the motion towards equilibrium, nor the process of the change itself. Comparative statics is commonly used to study changes in supply and demand when analyzing a single market, and to study changes in monetary or fiscal policy when analyzing the whole economy. Comparative statics is a tool of analysis in microeconomics (including general equilibrium analysis) and macroeconomics. Comparative statics was formalized by John R. Hicks (1939) and Paul A. Samuelson (1947) (Kehoe, 1987, p. 517) but was presented graphically from at least the 1870s. For models of stable equilibrium rates of change, such as the neoclassical growth model, comparative dynamics is the counterpart of comparative statics

Study on Mechanical Performance of Prestressed UHPFRC U-Beam Bridges

Eugen Brühwiler

The forms of U-shaped UHPFRC beams have not been investigated for the highway footbridge. Compared with the traditional section forms, the U-shaped UHPFRC beams can reduce the material consumption under the condition of providing the same bearing capacity. Furthermore, prestressed U-shaped UHPFRC beams are rarely reported in the existing research. This paper explores the flexural behavior of prestressed ultrahigh-performance fiber-reinforced concrete (UHPFRC) beam bridge having unique design and the material properties of prestressed reinforcement combined with UHPFRC. Based on the unique shape of the U beam, the flexural performance test of the full-scale model of the prestressed UHPFRC U beam is conducted. Then, the finite element model considering material nonlinearity and structural ductility is established using Midas FEA software. Finally, the failure mode, failure process, cracking moment, ultimate moment, and strain of the full-scale model are studied. The calculation formulas of the flexural capacity of UHPFRC U beam considering ductile failure are derived. The comparative analysis results show that the prestressed UHPFRC U beam has an excellent flexural performance. The bending failure of a U-shaped beam belongs to the group of ductile failures, which is characterized by the main crack along the central rib and the loading center, which is accompanied by multiple microcracks. The failure process can be divided into four stages: linear deformation, microcracks development, main cracks development, and bearing capacity decline. The incorporation of steel fiber and the interaction between UHPFRC and reinforcement can effectively reduce the development of cracks. The U-beam bending moment is 50-55% of the ultimate bending moment. In the UHPFRC bridge design, the deformation can be used as a control index, and material advantages of the UHPFRC can be used to a certain extent. The strain-hardening characteristics of the UHPFRC are obvious in the loading process. The finite element analysis results show that the maximum strain value appears at the central rib, followed by the transverse strain value of the bottom plate, while the minimum strain is the longitudinal strain value of the bottom plate. The deformation of the rib plate is the largest, and the strain of the other measuring points changes slowly. The farther away from the center the measurement point is, the slower its strain changes. Therefore, the load is mainly caused by the central rib and the loading center plate. With the increase in the deformation, the load on both sides continuously moves to the central rib along the plate surface. This study can provide a useful reference for theoretical analysis and design of prestressed U-UHPFRC bridges.

2021

Study on Mechanical Performance of Prestressed UHPFRC U-Beam Bridges

Eugen Brühwiler

2021